Stat 104 Section Notes 3
Problem Solutions
1a) I have 5 M&M’s left in the bag: 2 blue, 2 red, and 1 yellow.
I plan on eating two more, and
leaving the others in the bag.
a)
S = {(b
1
,b
2
), (b
1
,r
1
), (b
2
,r
1
), (b
1
,r
2
), (b
2
,r
2
), (b
1
,y), (b
2
,y), (r
1
, y), (r
2
,y), (r
1
,r
2
)}
b) Describe the set of events for:
A
:
A = {(b
1
,r
1
), (b
2
,r
1
), (b
1
,r
2
), (b
2
,r
2
), (b
1
,y), (b
2
,y), (r
1
, y), (r
2
,y)}
B
:
B = {(b
1
,b
2
), (b
1
,r
1
), (b
2
,r
1
), (b
1
,r
2
), (b
2
,r
2
), (b
1
,y), (b
2
,y)}
c) What is the probability of:
A:
B:
*Note: these simple probabilities could be calculated because we took some effort in
defining our sample space carefully so that each element was equally like to occur.
d) Are
A
&
B
disjoint? _
No
__ How do you know?
Because there are elements in both A and B (aka, the intersection is not empty).
Disjoint means the 2two events have nothing in common, but these two events certainly
do.
e) Describe (in words and in terms of outcomes) the intersection of
A
&
B
?
and the union,
A
or
B
?
A
and
B
= {(b
1
,r
1
), (b
2
,r
1
), (b
1
,r
2
), (b
2
,r
2
), (b
1
,y), (b
2
,y)}
A
and
B
= {(b
1
,b
2
), (b
1
,r
1
), (b
2
,r
1
), (b
1
,r
2
), (b
2
,r
2
), (b
1
,y), (b
2
,y), (r
1
, y), (r
2
,y)}
f) What is the probability of
A
&
B
?
A
or
B
?
g) Are